Furthermore, using the average Es extracted from Fig. REF (d) and Fig. REF (d), we can approximately compute the local shear stresses induced by the curing of PDMS and the polymerization of cyanoacrylate respectively. In order to convert between the stress representations in NV physics and SI system, we referred to some previous theoretical calculations [1]}, [2]}, [3]} and introduced the following additional assumptions. First, the axial (normal) forces on the surfaces of a ND are negligible, since our measurement results show insignificant changes in D and hence the local pressure during the chemical processes. Second, the shear (tangential) forces on the surfaces of an ND are assumed, for simplicity, to have an equal probability of being in any particular direction, because we believe that the shear forces are random in direction inside our chosen materials. Indeed, it is possible to determine the components of the full stress tensor, but it requires a well-controlled source of external magnetic field. Third, we treat our system isotropically. Since we have no information on the angle between the NV axis and the stress direction, we cannot precisely determine the components of the shear stress. Nonetheless, the stress susceptibility parameters, \(a_{1} = 4.86(2), a_{2} = -3.7(2), 2b = -2.3(3), \text{and } 2c = 3.5(3)\)  in units of MHz/GPa [2]}, do not differ by much in terms of magnitude. Therefore, for simplicity, we assume \(a = b = c = 1.75\)  MHz/GPa which means the ODMR response to the stress environment is isotropic. To precisely evaluate the local shear stress with respect to each axis, a well-controlled source of external magnetic field is, again, required. For PDMS, with the average E measured to be 0.1 MHz, the local shear stress induced by curing is calculated to be about 29.6 MPa. According to a bulk tensile test done by Johnston et al. [5]}, the ultimate tensile strength (UTS) of PDMS is 5.13 \(\pm \)  0.55 MPa at room temperature, thus the local shear stress obtained by our methodology is around 5.8 times larger. Likewise for AA glue, the average Es measured by 1 µm- and 100 nm-NDs are about 0.35 and 0.5 MHz respectively, so the corresponding calculated values of local shear stress are about 104 and 148 MPa. As stated in the specification from the manufacturer, a bulk sample of an instant adhesive that is similar to our AA glue has a UTS of about 31.7 MPa, so the local shear stresses deduced from our 1 µm-ND and 100 nm-ND data sets are about 3.3 and 4.7 times larger respectively. Here, both the PDMS and AA glue experiments reveal that the local accumulation of shear stress is quite strong. In fact, the local shear stress built up during the chemical processes can be considered as the internal tension in the amorphous solids. When experiencing a tensile load that exceeds the internal tension, the bulk solid starts fracturing. Thus, the local shear stress we obtained should be close to the UTS determined in bulk tensile tests. Nonetheless, our calculated local values are a few times greater than the bulk values. This difference may be attributed to the aforementioned assumptions, especially the approximation of an isotropic response from the ODMR spectrum to the stress environment. Meanwhile, we have observed a correlation between E and FWHM in the ODMR spectrum, meaning that the change in E reflects the variation in not only the local shear stress, but also the FWHM (decoherence time). Hence, interpreting the average E solely as the local shear stress accumulated would have been an over-estimation in our calculation. To conclude, despite being approximate values, we are able to microscopically probe the local shear stress inside PDMS and AA glue.
